This lab was designed in 1995 for "A Day in the Life of a Student in the 21st Century" - a teleconference with the US House committees on science, economics, and educational opportunities.

Purpose

The purpose of this lab is to produce an oscillation that has a varying amplitude and period. As the sand leaks from the funnel, the period of the spring's oscillation changes

since the mass is constantly decreasing. Moreover, the spring's amplitude also changes as more and more sand leaves the funnel.

A typical graph of this type of oscillation would look like the following sample.

Procedure (set-up)

Under the Start Menu go to Programs, Math, Logger Pro 3.1 to launch the program. Logger Pro should automatically set up the graphs according to the connected sensor. With the Motion Detector properly connected, the program should display graphs of position vs time and velocity vs time. Press Collect to test your connections. Make sure that you are collecting data to at least 3 decimal places.

A second member should verify that the probe is looking at the blue cardboard attached to the top of the funnel - only slight adjustments should be necessary! He/she should then fill the funnel with sand, keeping a finger over the exit hole so that the sand does not immediately run back out, and use the counterweights (slotted masses) to level the cardboard. The purpose of the box is to catch the sand as it leaves the funnel, so please make sure that it is in place before beginning the experiment. Verify that the probe is seeing the cardboard by moving the filled funnel carefully up and down -- DO NOT USE LARGE AMPLITUDES! 5-6 cm is MORE THAN ENOUGH! When everything is working, your are ready to start collecting data.

Procedure (data collection)

Since the sand leaves quickly, the probe should be started first. Try to release your spring with a small steady amplitude and a minimal amount of rotation (twisting). Watch your graphs. The oscillations should minimally have either a constant set of smooth crests OR smooth troughs -- it is not absolutely necessary to have perfect oscillations in both places.

With the completion of each trial, highlight a "good section" of your position vs time graph. The data selected will be highlighted in the accompanying data table. Copy and paste your data into an EXCEL spreadsheet. Rename the sheet Data I.

Carefully refill the funnel to the same level as in your first trial and obtain a second trial. Save this data on a second sheet in the same spreadsheet as Data II.

Finally, refill your funnel to the same level one last time. Record the height of the cardboard. Then record how much time it takes for all of the sand to flow out as it oscillates. Finally, record the final height of the carboard after the funnel is empty and has stopped vibrating.

Run your trials as accurately AND quickly as possible, remember that at least one other group needs to use your lab station before the period is over. When you are finished with both trials, leave the spring & funnel suspended and the sand in the box. Please sweep up and return any sand which got scattered onto the table back to the box. Clear your data from Logger Pro so that the next group can begin.

Analysis

Using your best spreadsheet data from either Trial I or Trial II, record the times and locations of 6 consecutive crests and troughs. Calculate the intermediate equilibrium positions, and then state the amplitude of each crest and trough.

crest/trough

time

position

equilibrium

amplitude

#1

#2

#3

#4

#5

#6

Did the amplitude of the sand spring's oscillations steadily decrease? Support your choice numerically.

calibration

loaded height

empty height

mass of sand

total time

spring constant

Using your time data from Chart #1, fill out the following chart regarding periods and average mass.

interval

period

mass

1-2

2-3

3-4

4-5

5-6

Did the period of the sand spring's oscillations steadily decrease? Support your choice numerically.

Based on the period data calculated in the table above, was the average amount of mass decreasing steadily? Support your choice numerically.

Using your data from emptying the sand spring, at what rate were you expecting the mass to change each second?

Calculate the percent difference between these two rates of mass change.

State a source of error that might justify the percent difference you calculated in the previous question.